Question 126752
If you have 5 points, you can make 4 lines from the first point to each of the others.  Then you also have 4 lines from the second point to each of the others, but you have already accounted for one of those 4 lines in the 4 lines from the first point, so you can only create 3 new ones.  Similarly, from the 3rd point you can only create 2 new lines, and from the 4th point, only 1 new line.  Finally, when you get to the 5th point, all possible lines have been created, and you can create no new lines.

4 + 3 + 2 + 1 + 0 = 10.


{{{drawing(480,480,0,12,0,12,
line(4,1,8,1),
line(8,1,11,6),
line(11,6,6,10),
line(6,10,1,6),
line(1,6,4,1),
line(4,1,11,6),
line(4,1,6,10),
line(8,1,6,10),
line(8,1,1,6),
line(1,6,11,6)

)}}}